Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in JAVA):

Solution:
import java.util.ArrayList;
import java.util.Collections;
import java.util.Scanner;

/**
 * Created by mostafa on 5/18/17.
 */
public class R414B {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int h = sc.nextInt();
        ArrayList<Double> ans = new ArrayList<>();
        double a = 0.5 * h / n;
        double prev = 1;
        double curH = h;
        for(int i = 0; i < n - 1; i++) {
            double low = 0;
            double high = prev;
            double hi = 0, base = 0;
            for(int j = 0; j < 100; j++) {
                base = (low + high) / 2;
                hi = curH * (prev - base) / prev;
                double area = 0.5 * (base + prev) * hi;
                if(area > a)
                    low = base;
                else
                    high = base;
            }

            curH -= hi;
            prev = base;
            ans.add(curH);
        }

        Collections.reverse(ans);

        for(double ai : ans) {
            System.out.print(ai + " ");
        }

        System.out.println();
    }
}